login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Sum of the cubes of the first n noncubefree numbers.
1

%I #19 Feb 20 2024 02:32:03

%S 0,512,4608,18432,38115,70883,134883,245475,402939,578555,840699,

%T 1213947,1725947,2257388,2938860,3823596,4948460,6208172,7613100,

%U 9341100,11294225,13391377,15851752,18367208,21353192,24865000,28961000

%N Sum of the cubes of the first n noncubefree numbers.

%F a(n) = Sum_{k=1..n} A046099(k)^3.

%F a(n) ~ c * n^4, where c = (zeta(3)/(zeta(3)-1))^3/4 = 52.6373493984... . - _Amiram Eldar_, Feb 20 2024

%e a(10) = 8^3 + 16^3 + 24^3 + 27^3 + 32^3 + 40^3 + 48^3 + 54^3 + 56^3 + 64^3 = 840699.

%t noncubeFreeQ[n_] := Max[FactorInteger[n][[;; , 2]]] > 2; Join[{0}, Accumulate[Select[Range[200], noncubeFreeQ]^3]] (* _Amiram Eldar_, Feb 20 2024 *)

%Y Cf. A046099, A114286.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Nov 20 2005